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Singular values and bounded Siegel disks
Published online by Cambridge University Press: 25 May 2017
Abstract
Let f be an entire transcendental function of finite order and Δ be a forward invariant bounded Siegel disk for f with rotation number in Herman's class $\mathcal{H}$. We show that if f has two singular values with bounded orbit, then the boundary of Δ contains a critical point. We also give a criterion under which the critical point in question is recurrent. We actually prove a more general theorem with less restrictive hypotheses, from which these results follow.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 165 , Issue 2 , September 2018 , pp. 249 - 265
- Copyright
- Copyright © Cambridge Philosophical Society 2017
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